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Fixing Challenge Rating
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<blockquote data-quote="NotAYakk" data-source="post: 9284590" data-attributes="member: 72555"><p>A creature that acts twice and deals 10 damage per action isn't substantially different than a creature that acts once, and does 20 damage on that action.</p><p></p><p>"Action Economy" matters when actions don't deal damage, and various forms of action nullification that scales better on fewer targets.</p><p></p><p>Like, if you can take a creature and say "you don't act next turn" as your action; then it doesn't matter if their action would do 1 billion damage, you just traded your action for theirs. But even in softer cases, like "I knocked you prone and pushed you 30' away" - the target gets to do an action, but it is reduced in scope and choice. Or even "I used my action to give all my allies advantage" - the more creatures on your side you have, the lower that cost is and the bigger the boost.</p><p></p><p>But most of the impact of why 2 monsters is more dangerous than 1 is that a natural way to measure a monster is its level. And if HP and damage are roughly proportional to level, then two level 5 monsters are going to each have half the HP and half the damage of a level 10 monster. If the level 5 monster fights the level 10 monster one-on-one, it will only drain 1/4 of the level 10 monster's HP -- but if it is 2:1 it goes up to 3/4 of the level 10 monster's HP. Twice as many monsters made that side 3 times as dangerous!</p><p></p><p>This comes from the fact that scaling both offence <em>and</em> defence has a quadratic impact on power, not a linear one, but we treated it as if it was linear. When you group monsters, the impact is not quite quadratic, because groups of monsters are subject to attrition in combat. A decent naive model is that the groups of monsters are subject to a triangular-shaped attrition over combat, with the other side focus-firing down one and eliminating it then moving onto the next.</p><p></p><p>Another model is to assume the other side uses AOE damage, or a combination of focus fire and AOE. As it happens you can model sub-one-shot AOE damage as doing focus fire damage to 1 target, and 0.5x value damage to all secondary targets, and you get a very similar amounts of total enemy damage done - ie, you can change how you model AOE damage, and it starts behaving (model-wise) as if it was single-target damage.</p><p></p><p>Like, you have 3 monsters each with 5 HP. You do 1 HP per attack. You take 3*5 + 2*5 + 1*5 damage, a total of 30. You add someone able to do 1 point of AOE damage at the start of the fight. You now take 3*4+2*4+1*4 = a total of 24 damage. Alternatively, you add someone who does 2 points of single target damage at the start of the fight. You now take 3*3+2*5+1*5 a total of ... 24 damage. The 2 points of focus-fire damage had the same impact as 1 point of aoe damage on 3 targets - 1 point on primary target, plus 2 * 0.5 on secondary targets = 2 points of effectiveness.</p><p></p><p>That 1x on primary 0.5 on secondary happens to fall out of the math of the area of a discrete triangle. I'd been using it as a heuristic for a while before I realized it was actually sound and grounded in the math, which amused me.</p></blockquote><p></p>
[QUOTE="NotAYakk, post: 9284590, member: 72555"] A creature that acts twice and deals 10 damage per action isn't substantially different than a creature that acts once, and does 20 damage on that action. "Action Economy" matters when actions don't deal damage, and various forms of action nullification that scales better on fewer targets. Like, if you can take a creature and say "you don't act next turn" as your action; then it doesn't matter if their action would do 1 billion damage, you just traded your action for theirs. But even in softer cases, like "I knocked you prone and pushed you 30' away" - the target gets to do an action, but it is reduced in scope and choice. Or even "I used my action to give all my allies advantage" - the more creatures on your side you have, the lower that cost is and the bigger the boost. But most of the impact of why 2 monsters is more dangerous than 1 is that a natural way to measure a monster is its level. And if HP and damage are roughly proportional to level, then two level 5 monsters are going to each have half the HP and half the damage of a level 10 monster. If the level 5 monster fights the level 10 monster one-on-one, it will only drain 1/4 of the level 10 monster's HP -- but if it is 2:1 it goes up to 3/4 of the level 10 monster's HP. Twice as many monsters made that side 3 times as dangerous! This comes from the fact that scaling both offence [I]and[/I] defence has a quadratic impact on power, not a linear one, but we treated it as if it was linear. When you group monsters, the impact is not quite quadratic, because groups of monsters are subject to attrition in combat. A decent naive model is that the groups of monsters are subject to a triangular-shaped attrition over combat, with the other side focus-firing down one and eliminating it then moving onto the next. Another model is to assume the other side uses AOE damage, or a combination of focus fire and AOE. As it happens you can model sub-one-shot AOE damage as doing focus fire damage to 1 target, and 0.5x value damage to all secondary targets, and you get a very similar amounts of total enemy damage done - ie, you can change how you model AOE damage, and it starts behaving (model-wise) as if it was single-target damage. Like, you have 3 monsters each with 5 HP. You do 1 HP per attack. You take 3*5 + 2*5 + 1*5 damage, a total of 30. You add someone able to do 1 point of AOE damage at the start of the fight. You now take 3*4+2*4+1*4 = a total of 24 damage. Alternatively, you add someone who does 2 points of single target damage at the start of the fight. You now take 3*3+2*5+1*5 a total of ... 24 damage. The 2 points of focus-fire damage had the same impact as 1 point of aoe damage on 3 targets - 1 point on primary target, plus 2 * 0.5 on secondary targets = 2 points of effectiveness. That 1x on primary 0.5 on secondary happens to fall out of the math of the area of a discrete triangle. I'd been using it as a heuristic for a while before I realized it was actually sound and grounded in the math, which amused me. [/QUOTE]
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